The lower bound confidence limit for variance from a normal distribution is:
The upper bound confidence limit for variance from a normal distribution is:
To obtain the confidence interval for the standard deviation, take the square root of the above equations.
The lower margin of error equals −1 × (lower bound confidence limit). The upper margin of error equals the upper bound confidence limit.
To solve for n for variance, calculate the minimum n such that:
(S2 – S2L) ≤ ME and (S2U – S2) ≤ ME
To solve for n for standard deviation, calculate the minimum n such that:
(S – SL) ≤ ME and (SU – S) ≤ ME
| n ||sample size|
| s2 ||sample variance|
| Χ2 p ||upper 100pth percentile point on a chi-square distribution with (n – 1) degrees of freedom|
| S ||planning value|
|ME||margin of error|